A261710 Decimal expansion of Integral_{0..Pi/2} x^2*tan(x)*log(sin(x)) dx (negated).

2, 2, 7, 7, 1, 4, 4, 7, 9, 9, 7, 9, 5, 7, 9, 1, 6, 0, 6, 0, 6, 5, 5, 8, 0, 2, 6, 2, 6, 2, 1, 4, 7, 0, 3, 3, 4, 9, 3, 8, 4, 3, 9, 1, 3, 5, 5, 5, 0, 3, 1, 7, 2, 8, 8, 7, 1, 9, 1, 7, 9, 3, 4, 9, 0, 0, 0, 5, 1, 3, 3, 0, 4, 4, 3, 4, 8, 0, 8, 0, 7, 7, 2, 6, 1, 2, 6, 6, 3, 7, 0, 0, 7, 9, 8, 7, 0, 1, 5, 4, 4, 3, 6, 6, 4

Offset

0,1

Comments

This integral appears in the expression of the 3rd moment of the distribution of the number of vertices of Goudsmit-Miles random polygonal cells.

Links

Table of n, a(n) for n=0..104.

Steven R. Finch, Random Triangles V, December 22, 2010, p. 9. [Cached copy, with permission of the author]

J. C. Tanner, Polygons Formed by Random Lines in a Plane: Some Further Results, Journal of Applied Probability, Vol. 20, No. 4 (Dec., 1983), pp. 778-787. See Eq. 7, p. 783.

Example

-0.2277144799795791606065580262621470334938439135550317288719179349...

Mathematica

NIntegrate[x^2*Tan[x]*Log[Sin[x]], {x, 0, Pi/2}, WorkingPrecision -> 105] // RealDigits // First

Crossrefs

Sequence in context: A142070 A152825 A347073 * A064288 A054085 A357412

Adjacent sequences: A261707 A261708 A261709 * A261711 A261712 A261713

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 29 2015

Status

approved